Optimal. Leaf size=31 \[ \frac{\sqrt{1-x^4}}{2}+\frac{1}{2 \sqrt{1-x^4}} \]
[Out]
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Rubi [A] time = 0.0393266, antiderivative size = 31, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.133 \[ \frac{\sqrt{1-x^4}}{2}+\frac{1}{2 \sqrt{1-x^4}} \]
Antiderivative was successfully verified.
[In] Int[x^7/(1 - x^4)^(3/2),x]
[Out]
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Rubi in Sympy [A] time = 4.54226, size = 20, normalized size = 0.65 \[ \frac{\sqrt{- x^{4} + 1}}{2} + \frac{1}{2 \sqrt{- x^{4} + 1}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**7/(-x**4+1)**(3/2),x)
[Out]
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Mathematica [A] time = 0.0110737, size = 22, normalized size = 0.71 \[ \frac{2-x^4}{2 \sqrt{1-x^4}} \]
Antiderivative was successfully verified.
[In] Integrate[x^7/(1 - x^4)^(3/2),x]
[Out]
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Maple [A] time = 0.006, size = 28, normalized size = 0.9 \[{\frac{ \left ( -1+x \right ) \left ( 1+x \right ) \left ({x}^{2}+1 \right ) \left ({x}^{4}-2 \right ) }{2} \left ( -{x}^{4}+1 \right ) ^{-{\frac{3}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^7/(-x^4+1)^(3/2),x)
[Out]
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Maxima [A] time = 1.4395, size = 31, normalized size = 1. \[ \frac{1}{2} \, \sqrt{-x^{4} + 1} + \frac{1}{2 \, \sqrt{-x^{4} + 1}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^7/(-x^4 + 1)^(3/2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.284799, size = 22, normalized size = 0.71 \[ -\frac{x^{4} - 2}{2 \, \sqrt{-x^{4} + 1}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^7/(-x^4 + 1)^(3/2),x, algorithm="fricas")
[Out]
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Sympy [A] time = 2.3447, size = 22, normalized size = 0.71 \[ - \frac{x^{4}}{2 \sqrt{- x^{4} + 1}} + \frac{1}{\sqrt{- x^{4} + 1}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**7/(-x**4+1)**(3/2),x)
[Out]
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GIAC/XCAS [A] time = 0.211369, size = 31, normalized size = 1. \[ \frac{1}{2} \, \sqrt{-x^{4} + 1} + \frac{1}{2 \, \sqrt{-x^{4} + 1}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^7/(-x^4 + 1)^(3/2),x, algorithm="giac")
[Out]